Elementary Estimators for Sparse Covariance Matrices and other Structured Moments
Authors: Eunho Yang, Aurelie Lozano, Pradeep Ravikumar
ICML 2014 | Conference PDF | Archive PDF | Plain Text | LLM Run Details
| Reproducibility Variable | Result | LLM Response |
|---|---|---|
| Research Type | Experimental | We illustrate the applicability of our framework via simulation and by applying it to two real-world problems, one on climate analysis, and the other on 3-D organization of chromosomes. 6. Experiments Simulation We first confirm the usefulness of our framework in the presence of superposition structures. Specifically, we focus on covariance estimation where the true covariance has a sparse plus low-rank structure. We consider Σ = Σ 1 + Σ 2, where Σ 1 = 0.5(1p1T p ). and Σ 2 = Ip/5 (0.2(151T 5 ) + 0.2I5), where denotes the Kronecker product. We perform 100 simulation runs. For each simulation run, we generate n = 100 observations from N(0, Σ ). We compare our Elem-Super-Moment estimator with the thresholding method of Bickel & Levina (2008a) and the well-conditioned estimator of Ledoit & Wolf (2003). For each method, the tuning parameters are set using 5-fold cross validation with Frobenius norm as described in Bickel & Levina (2008a). We consider p = 200, 400. As performance measures, we used the spectral, Frobenius, nuclear and matrix 1-norm of the difference between estimated and true covariance. The results presented in Table 1 show that Elem-Super-Moment clearly outperforms the other methods. |
| Researcher Affiliation | Collaboration | Eunho Yang EUNHO@CS.UTEXAS.EDU Department of Computer Science, The University of Texas, Austin, TX 78712, USA Aur elie C. Lozano ACLOZANO@US.IBM.COM IBM T.J. Watson Research Center, Yorktown Heights, NY 10598, USA Pradeep Ravikumar PRADEEPR@CS.UTEXAS.EDU Department of Computer Science, The University of Texas, Austin, TX 78712, USA |
| Pseudocode | No | The paper does not contain any structured pseudocode or algorithm blocks. |
| Open Source Code | No | The paper does not provide an explicit statement or a link indicating that the source code for the described methodology is publicly available. |
| Open Datasets | Yes | Climate dataset We used 4times daily surface temperature data from NCEP/NCAR Reanalysis 1. ... Hi-C dataset We also illustrate the usefulness of our class of estimators on data from Hi-C, a very recent methodology to study the 3-D architecture of genomes. ... We consider two Hi-C datasets taken from Lieberman-Aiden et al. (2009) |
| Dataset Splits | Yes | For each method, the tuning parameters are set using 5-fold cross validation with Frobenius norm as described in Bickel & Levina (2008a). |
| Hardware Specification | No | The paper does not provide specific hardware details (exact GPU/CPU models, processor types with speeds, or memory amounts) used for running its experiments. |
| Software Dependencies | No | The paper does not provide specific ancillary software details, such as library or solver names with version numbers, needed to replicate the experiment. |
| Experiment Setup | No | The paper does not provide specific experimental setup details, such as concrete hyperparameter values or detailed training configurations for the models. |